Yes, you can do it. It's called a ticketless package. I have always had to call to do it, but have heard of people here on the DIS that have been able to book it online.
The thing is, if you currently have a room only you can't just add Dining. You have to switch to a package, albeit without tickets, which will require a new $200 deposit. Room Only and Packages are on 2 different systems so any $$ paid on the room only can't be transferred, it will have to be refunded.
Unfortunately, you will have to call back and hopefully get a phone CM that knows what they're doing. Sometimes it's taken me 3-4 calls to get it done, but it can be done.